期权管理知识讲解-英文版

Reading,HullChapter1:Perhapsre-readthesectiononoptionswhichisinsections1.51,10.HullChapter7:Thisstartswiththebasicsofoptionsandthengoesonintothespecificdetailsoftrading.Readupto7.4forthecrucialdetailsandtherestifyourestillinterested.HullChapter8:Thisisquiteinterestingbutperhapsalittletechnicalatthispointintime.Themostimportantpartasregardsthelectureis8.4andperhapsisinterestingtoseethecrucialfactorsindeterminingthepriceofanoptionandwillbeusefulforfuturereference(i.e.thelasttwoweeks).HullChapter9:Quiteanicechapterexplainingoptionsstrategies,Imgoingtoworkthroughasampleoftheseinclasssoitmaybeusefultofamililiariseyourselveswiththeprincipalstrategies.,Reading,HBRArticle:StockoptionshavehadaverynegativepressoflateandherewehaveNobelprizewinnerRobertMertonandotherhigh-profileacademicsdiscussingsomeoftheissuesandargueforstockoptionstobeputonthebalancesheet.Thiswillactuallycomeintoforceatthestartof2005.,Futurescontractsarecontractswhichcostnothingtoenter.Thisisbecauseifyouareinthelongpositionyougainwhenthespotpriceoftheunderlyingasset,S,rises,youalsolosewhenthepricegoesdown(andviceversawiththeshortposition).Anoptionissimilarinmanywaystoafuturescontractinthatyouhavetherighttobuy(orsell)atacertainpriceinthefuture(thistimeitiscalledtheexerciseprice).However,theprincipaldifferenceisthatyoudonthavetheobligationtobuyatthispriceyouhavetheoptionaswhetherornotyouchoosetobuy(orsell)atthisprice.Clearlyyouwillhavetopaysomepremiumforthisprivilege.Howmuch?,Options:Introduction,Whyoptions?,Optionscanagainbeusedforthreemainpurposes:hedging,speculatingandarbitraging.Anoptionenablesyoutohedgeagainstadversemarketmovements(e.g.priceofoil,priceofcorn,stockmarketvalue,interestratechanges)without,necessarily,limitingyourpotentialgainshouldthemarketactuallymoveinyourfavour.Justlikewithafuturescontractanoptionenablesyoutoleverageyourpositionandhencemakeiteasiertospeculateonmarketmovements.Againwithoptionsasthefinancialinstrumentsbecomemorecomplexthentherearemorearbitrageopportunitiestoexploit.,Options:definitions,Anoptiongivestheholderoftheoptiontheright,butnottheobligationtobuyaneconomicgood(usuallycalledtheunderlyingasset),ataspecificpointintime(theexpirydate),foraspecificprice(theexerciseprice).Thepartywhoboughttheoptionissaidtobeinthelongposition,thepartywhosold(orwrote)theoptionissaidtobeintheshortposition.ACallOptiongivestheholderoftheoptiontheright,butnottheobligation,tobuytheunderlyingasset.APutOptiongivestheholderoftheoptiontheright,butnottheobligation,toselltheunderlyingasset.,Options:Types,Therearetwomaintypesofoptions:Europeanoptions:Europeanoptionscanonlybeexercisedontheexpirydate.Americanoptions:Americanoptionscanbeexercisedatanytimebetweenthedateofpurchaseandtheexpirydate.Thesenameshavenogeographicalsignificance,henceitispossibletobuyAmericanoptionsonEuropeanoptionsexchanges.MosttradedoptionsareAmericanoptions,althoughwewillstartourdiscussionbyassumingthatalloptionsareEuropean.,Options:Example,ConsiderbothcallandputoptionsonMicrosoftshares,expiringonMarch20,2004.Bothhaveexercisepricesof$25andeachoptionenablestheholdertobuyorselltheMicrosoftsharesatthisprice.ThecurrentvalueofMicrosoftsharesis$27.03.Calloptionsarecurrentlypricedat$2.20andputoptionsat$0.13.MicrosoftcurrentoptionpricesOptionsProductSpecificationsThepayoffsfromtheseoptionsfordifferentvaluesoftheMicrosoftsharesareasfollows:,Options:example,Options:example,ClearlyisthevalueofaMicrosoftshareexceedstheexercisepricesthentheholderofthecalloptionwillexercisehisrighttoexerciseandmakeaprofitofthesharepricelesstheexerciseprice.Ifitislessthenhewillnot,inthiscasetheoptionexpiresworthless.InthecaseoftheputoptiontheiftheMicrosoftsharepricedropsbelowtheexercisepricethenshewillexerciseandreceivethedifferencebetweentheseprices.Ifitismorethentheoptionexpiresworthless.Fromthiswenotethatoptionsmustalwayshavepositiveorzerovalueastheleasttheycaneverbeworthiszero.,Options:leverage,Optionsonindividualsharesareactually100shares.NoticethatifthevalueofMicrosoftsharesatexpiryat$30thentheholderofthecalloptionmakesaprofitof$500$220=$280orareturnof280/220=127%.Ifinsteadhewouldhavespentthismoneyonbuyingthesharesthenthereturnwouldhavebeenonly(3027.03)/30=9.8%.Thisisanexampleoftheleverageaninvestorcanobtainfrombuyingoptionsratherthantheunderlyingassetsthemselves.Noticehoweverthatisthesharepriceisonly$25,thentheinvestorhasmadereturnsof100%(astheoptionexpiresworthless)comparedtoalossof7.5%frombuyingtheshares.,Payofffromacalloption,Itispossibletodepictthepayoffsfromthiscalloptiongraphically:,25,Sharepriceatexpiry,Calloptionvalueatexpiry(PAYOFF),Payofffromaputoption,andalsotheputoption:,25,Sharepriceatexpiry,Putoptionvalueatexpiry(PAYOFF),Profitdiagrams,Noticethatthesegraphsdonotincludethepremiumwhichhasbeenpaidforthisoption,ifweincludetheamountpaidthenwhatweseeisthefollowinggraphs:,25,25,-$2.20,-$0.13,ProfitfrombuyingtheMicrosoftcalloptionfor$2.20,ProfitfrombuyingtheMicrosoftputoptionfor$0.13,Writing(orselling)options,Wehaveseenwhathappenswhenyoubuycallorputoptions.Whataboutforthepersonwhohassold(orwritten)theseoptions?Ifyouwriteacalloptionthenitmeansthat,first,youreceivetheoptionpremium.Attheexpiryoftheoptionthenyouareobligedtoselltheunderlyingassetattheexercisepriceiftheholderwishestobuyit.Inthiscaseyouloseoutbythedifferenceintheprices,ifhowever,theydontexercisetheiroptionthenyousimplykeepthepremium.Notethatthesetransactionsarezerosumgames,whatevertheholdergains,thewriterloses.Itissimilarforaputoptiononlyyouhavetobuyattheexercisepriceiftheholderwantstosell.,Payoffwhenwritingoptions,ReturningtotheMicrosoftexample,thepayoffsareasfollows:,Payoffsfromwritingoptions,InasimilarwaywecangraphicallydepictthepayoffsfromwritingcallandputoptionsonMicrosoft.,25,25,Sharepriceatexpiry,Sharepriceatexpiry,Payoffatexpiryfromwritingacalloption,Payoffatexpiryfromwritingaputoption,Profitfromwritingoptions,ItisalsotoseetheprofitfromwritingtheMicrosoftcallandputoptions:,25,25,Sharepriceatexpiry,Profitatexpiryfromwritingacalloption,Profitatexpiryfromwritingaputoption,$2.20,$0.13,Optionprinciples,Clearlybuyingandwriting(selling)optionsisazerosumgame.Everythingmadebythebuyerislostbythewriterandviceversa.Notethatbothbuyingcallsandsellingputsarebetsthatthemarketwillgoup.Buyingputsandwritingcallsarebetsthatthemarketwillgodown.ThisoptionwastreatedasifitwereaEuropeanoptionabutinrealitythisoptionwouldbeAmericanthusexercisableatanytime.Thiswouldmaketheanalysisslightlydifferentasyouwouldhavetoconsiderifthereareoptimaltimestoexercisetheoption.,Options:details,OnaregulatedexchangethenthecontractbetweenpartiesisagainsecuredbytheexchangeorbytheOptionClearingCorporation(OCC).Infactifyoubuyanoptionyoudonthaveacounterparty,ratheryouactuallybuyitfromtheexchangewhoitturnbuyoptionsfrompartieswhowanttosell.Itispossibletoterminateyouroptionpositionbeforeexpirysimplybyselling(ifyouhadoriginallybought)orbuying(ifyouhadoriginallysold),youwillmake(orlose)thedifferencebetweenthepriceyouboughtorsoldatandthepricetoday.,Optionsmoreterminology,Near-the-moneyorat-the-moneyareoptionswheretheexercisepriceisclosetothecurrentshareprice.Out-of-the-moneyoptionsareoptionswhereimmediateexercisewouldproduceanegativepayoff(i.ethesharepriceishigherthantheexercisepriceforaputoption).In-the-moneyoptionsareoptionswhereimmediateexercisewouldproduceapositivepayoff(i.e.thesharepriceishigherthantheexercisepriceforacalloption).LEAPSarelongtermoptionsonindividualsharesorstockindices.FLEXoptionsareoptionswheretheinvestorsdeterminetheexercisepriceandexpirydates(Seepressreleasedocumentinlecture).,Optiontradingstrategies,Therearemanywaysofcombiningdifferenttypesofoptionscontractstosuitaninvestorsparticularbeliefaboutthemarketortohedgeaparticularrisk.Wewillworkthroughthreemaintypes(althoughtherearemanymoreespeciallywhenyouincludeexoticoptions),theseare:Protectivepositions.Spreads(verticalcall,butterfly)Straddles.ThesewillallbeexplainedusingCiscosharesastheunderlyingasset(althoughthepricesarenotactuallyrealprices),Theprotectiveput:definition,AssumethatyouownCiscosharesbutyouareveryworriedaboutalargeloss.Itscurrentsharepriceis$92.875.ToprotectagainstaseveredropinthesharepriceyoubuyaputoptionexpiringinJulywithanexercisepriceof$95.Thiscurrentlycosts$10.25bringingyourtotalinvestmentto$103.125.Thepayoffisgivenonthenextpage.Noticethatyoulimityourdownsidelossto7.9%,butyoupayforthiswithdecreasingreturnsshouldthepricegoupsignificantly(e.g.26.1%ratherthan40%ifthesharepricereaches$130).,Protectiveput:results,Returnsbasedoncostof$92.875forshareplusaputcosting$10.25=$103.125.,Verticalcallspread:definition,Spreadsconsistofpositionswhereyouownportfoliosentirelyinoptions.Intheverticalcallspreadyoubuyacall(withexercisepriceX)andwriteacallwithahigherexercisepriceY).ThespreadiscalledaXYverticalcallspread.ConsidertheCiscoJuly95-100spread.Purchaseacallwithexerciseprice95(costof$11.25)andwriteacallwithexerciseprice100(recouping$9.125)whichcostsyou$2.125.Itisactuallypossibletosimplybuythespreadratherthanenteringintoboththepositions.Itisalsopossibletodothesamewithputsifyouhaveabearishviewoftheshare.,Verticalcallspreadpayoff,Returnbaseduponcostsof$11.25-$9.125=$2.125.,95-100Verticalspreadpayoff,95,Sharepriceatexpiry,Spreadvalueatexpiry(PAYOFF),100,5,Butterflyspread:definition,Abutterflyspreadconsistsonlyofoptions.TheyinvolvefouroptionpositionswiththesamematuritybutthreedifferentexercisespricesX,YandZ(whereX0AmericanoptionsmustbeworthatleastasmuchasEuropeanoptionsbecauseAmericanoptionscanbeexercisedatanytimei.e.itisaEuropeanoptionwithextraflexibility.AmericancallEuropeancallAmericanputEuropeanput,Put-Callparity,Themostusefulsimplerelationshipbetweencallandputoptionpricesistheputcallparity.Consider,forthesakeofanexample,Europeanputandcalloptionsonasharewithcurrentprice$50(payingnodividends),bothoptionshaveexercisepricesof$55andthesamematurity.Constructtwoportfolios:A:BuyoneEuropeanputoptionandalsobuytheshare.B:BuyoneEuropeancalloptionandinvestanamountofcashwhich,atexpiry,willhavevalueequaltotheexerciseprice($55).Thefollowingtabledemonstratesthattheybothhavethesamevalueatthematurityoftheoption.,Put-callparity:cashflows,PortfoliopayoffstoshowPut-callparity,exercisepriceis55,Put-callparity,Noticethatthefirstportfolioisoftentermedtheinsuranceportfolioastheportfoliocanneverhaveavaluelessthantheexerciseprice,$55inthiscase,whichmeansthattheholderofthisportfoliocanalwayssellthesharefor$55regardlessofitsprice.Clearlyregardlessofwhatthesharepriceisthenthesetwoportfoliosareequalinvalueatthematurityoftheoptions(regardlessofhowlongthisactuallyis).Ifthisistruethenthepresentvalueofthetwoportfoliosmustalsobethesame,otherwisetherewillbeanarbitrageopportunity.,Putcallparity:arbitrage,Assumethatthematurityoftheoptionsisoneyearandthatthecurrentsharepriceis$50andthe1-yearriskfreerateis1%.Thecurrentpriceoftheputoptionis$7,andthecurrentvalueoftheriskfreeassetis55/(1.01)=$54.46.Inthiscasethecalloptionshouldhavevalue$2.54(i.e.$7+$50-$54.46=$2.54).Whathappensifcalloptionsareactually$4?WellthevalueofportfolioAis$57andthevalueofportfolioBis$58.46.Youbuylowsellhighi.e.buytheputandtheshareandsellthecallandborrow$54.46for1year.Thisgivesyouaprofittodayof$2.54.Whatisyourcashflowattheendoftheyear?,Putcallparity:arbitrage,PayofffrombuyingportfolioAandsellingportfolioB,withexercisepriceof$55andmaturityof1year.,Put-callparity:result,Soyouarereceiving$2.54nowfornocost,hencethisisanarbitrageopportunity.Assuchtheseportfoliosmustbeequalinvalueatanypointpriortomaturitygivingthefollowingresult(whereXistheexerciseprice).EuropeanPut+Share=EuropeanCall+PresentvalueofXThiscanberearrangedtogivethearbitrageportfolio:Put+ShareCallPresentvalueofX=0Alsoitcanallowyoutodeterminethevalueofcallandputoptionsgiventhevalueoftheother:Put=Call+PresentvalueofXShareCall=Put+SharePresentvalueofX,Put-callparity:example,GivenourMicrosoftdata,doesput-callparityhold?Weassumethatthecurrentrisk-freerateis1.5%p.a,thereare250tradingdaysintheyearandgiventhatthecurrentsharepriceis$27.03andexercisepriceis$25.Thecurrentvalueoftheputoptionis$0.125givingCall=$0.125+$27.03$25e-0.015*30/250Call=$2.20Thuswiththeseassumptionsput-callparityholds.Notethatthereisachoiceofhowyoucalculatethepresentvalue,youcanusediscreteandcontinuouscompoundingbutwiththesetimescalesthenitisprobablyeasiertousecontinuouscompounding.,Put-callparity:Americanoptions,NotethatputcallparityalsoprovidesboundsforthevalueofEuropeancallandputoptions.Asweknowthatbothmustbeworthatleastzerothenthisgives:EuropeanCallSharePresentvalueofXEuropeanPutPresentvalueofXSheMicrosoftexample(assumingthesametimeandrisk-freerate)thenCall$27.03-$24.96=$2.07Thisprovidesuswithaveryinterestingresult,astheAmericancalloptionisworthatleastasmuchastheEuropeancallthenAmericancallSharePresentvalueofX,Put-callparity:Americanoptions,However,withanAmerica